COPYRIGHT 2014 STEEL JOIST INSTITUTE

REFERENCE MANUAL AND

SPREADSHEET USERS GUIDE

Joist Girder Moment Connections to the Weak Axis of Wide Flange

Columns

Version 1.0

Steel Joist Institute 234 W. Cheves Street Florence, SC 29501

Phone: (843) 407-4091 www.steeljoist.org

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Joist Girder Moment Connections to the Weak Axis of Wide Flange Columns A typical moment connection to the weak axis of a W shape is shown in Figure 1. The top plate transfers the top chord load to the column. The Joist Girder seat is a bracket connection. The weld connecting the bracket web to the column web is assumed to transfer only the vertical reaction (shear) of the Joist Girder to the column web. The horizontal plates transfer the horizontal forces from the bracket eccentric moment. They also prevent the bracket web plate from buckling. See Figure 2. The horizontal plates at the stabilizer plate transfer the bottom chord force to the flanges of the column and also prevent the stabilizer from buckling. See Figure 3. Shown in Figure 4 is the condition where Joist Girders frame to both sides of the column.

Figure 1: Weak Axis Connection

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Figure 2: Bracket Connection

Figure 3: Stabilizer Connection

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Figure 4: Joist Girders on both sides of the Column

Design Requirements:

For brevity, this Manual is presented in LRFD format. ASD design procedures follow in a parallel nature. Before using the SPREADSHEET the user should perform a structural analysis to determine that the column has the available strength to resist the applied loads. The user should also have a working knowledge of the AISC connection design requirements.

A. Top Plate Connection, Cap Plate and Cap Plate Weld: The required strength of the top plate is determined from the axial force in the top chord of the Joist Girder, Pu = Mr/de. Where, Mr is the required end moment of the Joist Girder, and de is taken as the distance from the top of the Joist Girder to the half depth of the bottom chord leg. Based on yielding, which generally controls, the required top plate area equals Pu/Fy ( = 0.9). The length of the plate can be determined based on the required length of fillet welds used to attach the plate to the

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column cap plate and the top chord. Shear lag must be checked per the 2010 AISC Specification Table D3.1 Shear Lag Factors for Connections to Tension Members. The SPREADSHEET requires the weld length to be a minimum of two times the width of the top plate for the connection of the top plate to the Joist Girder top chord. Based on Case 4 in the AISC Manual Table D3.1, U =1.0 for this condition. For the Top Plate connection to the column cap the strength of the top plate is reduced for any shear lag. The Joist Girder Manufacturer has the responsibility to check the top chord angles for shear lag. Case 2 from Table D3.1 is applicable for this check. For reference, the shear lag factor is calculated for the top chord based on the INPUT of the angle size. Shear lag factors greater than 0.92 do not have an effect on the Joist Girders. Providing longer length fillet welds will reduce shear lag effects.

Where Joist Girders frame to both sides of a column (Moment Interior W Column), the minimum weld requirement to each Joist Girder top chord is checked. The column shear yielding, plate thickness, and the weld required from the plate to the column are checked for the force delivered by the Joist Girder on each side of the column. These results are found under the heading, SUMMARY RESULTS for MOMENT CONNECTION. The minimum requirements for column shear yielding, plate thickness, and the weld required from the plate to the column sidewalls are based on the algebraic sum of the top chord forces in the top plate. These results are found under the heading COMBINED LEFT & RIGHT JOIST GIRDER RESULTS. The following checks are made in the SPREADSHEET for the Top Plate Connection, Cap Plate and Cap Plate Weld:

1. Check yielding ( = 0.9)

Top Plate - Yielding AISC D2-1

Rn = FyAplate 2. Check tensile rupture ( =0.75)

Top Plate - Tensile Rupture AISC D2-2

Shear lag at Joist Girder, U = 1.0 (Forced by the SPREADSHEET) Shear lag at the cap plate per Case 4 AISC Table D3.1

cp tp2W where cp equals the weld length on each side of the plate. therefore U= 1.0 Rn = UFuAplate

3. Shear yielding strength of the column ( = 0.9)

Column.- Shear Yielding

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The nominal shear strength, Vn, determined using the provisions of AISC Section G7

Vn = 0.6FyAfCv Af = 2bftf Cv= 1.0

For all W shapes with Fy 65 ksi, Cv = 1.0 The SPREADSHEET does not check the column web flange shear below the bottom chord of the Joist Girders.

NOTE: If the flanges do not have the available strength for shear, then a column with more flange area should be selected.

4. Determine the Joist Girder top chord shear lag factor Joist Girder - Shear Lag Case 2 AISC Table D3.1

xU 1

5. Weld strength between the Joist Girder and the top chord ( = 0.75) Weld - Top Plate to Joist Girder Top Chord AISC J2-3

Rn = (0.6)(FEXX)(0.707)wtc = kips/in. Strength = Rn = (2)( Rn)(Ltc)

6. Weld strength between the top plate and the column cap ( = 0.75)

Weld - Top Plate to Column Cap Plate AISC J2-3

Strength = Rn = (2)( Rn)(Lcp)

7. Weld strength between the column cap plate and the column flanges ( = 0.75) Column Cap Plate - Weld to Column Flanges AISC J2-3

Rn = (0.707)(wccp)(0.60)(FEXX)(2bf)

B. Bracket Connection (Stiffened Seated Connection):

The bracket connection consists of a vertical stiffener and top and bottom stiffener plates. The top plate is used for the seat. The bracket seat transfers the Joist Girder reaction to the stiffener. The stiffener transfers the vertical reaction (shear) to the column web. The moment created by the eccentricity of the reaction is transferred to the column flanges as a force couple in the top and bottom plates. The eccentricity is taken as the distance Ws - N/2.

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The seat width is determined from the minimum bearing length (N) from the SJI Standard Specifications for Joist Girders Section 1004.4 (b) Steel (SJI 2010).1

The following design provisions and checks are required:

1. AISC provisions indicate that when supporting beams, the stiffener thickness, ts should be equal to or greater than the thickness, tw of the supported beam web. Since Joist Girder seats are composed of two angles with typically a 1 in. gap between the angles this requirement does not apply. In lieu of this requirement a minimum stiffener and seat plate thickness of 1/2 in. is recommended.

2. Determine the maximum bracket height.

3. To prevent local buckling of the seat horizontal plates and the web of the bracket it is suggested that the plates have b/t and h/t values that comply with the AISC criteria for compact elements. (Local Buckling).

For the top and bottom plates of the bracket:

p y

b E 0.38t F

Case 11 AISC Table B4.1b

For the web of the bracket (vertical stiffener):

s y

h E 3.76t F

Case 15 AISC Table B4.1b

Where b is the width of the plate between the vertical stiffener and the flange of the column, h is the clear height of the stiffener between the horizontal plates, tp is the thickness of the seat plate and ts is the stiffener thickness.

4. Determine the seat plate thickness, tp, due to the Joist Girder reaction ( = 1.0) Seat Plate - Shear Yielding

u

py

Pt 2 N 0.6F

Eq.5-162

5. Determine the required thickness of the seat plate due to uplift ( = 0.9) Seat Plate - Uplift Loading The seat plate must also be checked for bending and shear from uplift reactions. The effective width of plate (beff) is determined by using a 45 degree projection from the bolt line to the face of the stiffener. beff cannot be greater than N. The available bolt uplift strength must be determined by the Engineer of Record or the Specifying

1Consult the SJI 2015 Specifications for revised minimum bearing lengths2 Equation from the SJI Technical Digest 11, Design of Lateral Load Resisting Frames Using Joist and Joist Girders

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Professional. Uplift bolt strength should be based on the Steel Joist Institutes Technical Digest 6, Design of Steel Joist Roofs to Resist Uplift Loads.

Based on a bolt gage (g) of 5 in. and using a 45 degree projection, the effective width in bending for the seat plate equals:

beff = 2(g - ts)/2 N = g - ts N

The nominal flexural strength Mn = FyZ 1.6My

Fybefftp2/4 1.6Fybefftp2/6 AISC F11-1 Lever arm = (g - ts)/2 Rn = 2Mn/Lever arm

The SPREADSHEET performs this calculation even if no uplift load case exists.

6. For gravity loads, the bearing strength on the stiffener contact area must satisfy the equation from the 2010 AISC Specification Chapter J Section J7(a) ( = 0.75) Stiffener - Bearing Strength on Contact Area

pbyn AF8.1R AISC J7-1

where, Apb = projected bearing area, in.2 (mm2) Fy = specified minimum yield stress of the stiffener plate, ksi (MPa).

7. Stiffener thickness to prevent vertical shear yielding ( = 1.0).

Stiffener - Shear Yielding

u

sy s

Rt 0.6F L

Eq. 5-172

where, Ru = the Joist Girder reaction, kips. Ls = stiffener length, in. ts = stiffener thickness, in.

8. Determine the required weld connecting the stiffener to the column web ( = 0.75).

Weld - Stiffener to Column Web Ru Rn Rn = (2)(0.75)(0.6)FExx(0.707)(ws)(Ls)

If the column web or vertical stiffener is not thick enough to develop the fillet weld, then a reduction in the strength of the fillet weld must be taken. The reduction factor applied to the weld strength is calculated as the thickness of the column web divided by the required thickness to develop the weld.

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9. Determine the required weld between the stiffener and the top and bottom plates. Weld - Stiffener to Seat/Bracket Plates

The weld that connects the stiffener to the top bracket plate is required to resist any uplift present, as well as the shear flow (q), due to bending in the bracket. The uplift force is resisted by an effective weld length below the joist girder seat equal to the bolt gage minus the stiffener plate thickness, but not to exceed the bearing length. The shear flow, q is determined from strength of materials equation, q = VQ/I. I and Q are calculated and reported under the BUILT-UP SEAT SECTION PROPERTIES in Cells R38 and R39. The uplift weld force and shear flow are then combined by the square root of the sum of the squares since they are acting perpendicular to one another. For simplicity the bottom plate weld requirements are assumed equal to the top plate requirements. The nominal strength of the welds, kips/in. is calculated from the equation: Rn = (2)(0.6)(FEXX)(0.707)(ws). Two (2) welds resist the shear.

If the seat plate or vertical stiffener is not thick enough to develop the fillet weld, then a reduction in the strength of the fillet weld must be taken. The reduction factor applied to the weld strength is calculated as the thickness of the seat plate or vertical stiffener divided by the required thickness to develop the weld.

10. Determine the strength of welds connecting the seat bracket plates to the column

flange, and the minimum thickness of the plates and column flange ( = 0.75). Weld - Seat/Bracket Plates to Column Flange.

The required shear on the welds is caused by the eccentricity of the load on the bracket. Four (4) welds resist the shear. Vr = (Ru)(Ws - N/2)/(Ls + tp) kips/top or bottom plate Rn = (4)(0.6)(FEXX)(0.707)(wp)[Weld Length] where: Weld Length = (bf - tw)/2 - k k = the corner clip = (k1 - tw/2) rounded up to the nearest in. Vr Rn

If the plate (or column flange) is not thick enough to develop the fillet weld, then a reduction in the strength of the fillet weld must be taken. The reduction factor applied to the weld strength is calculated as the thickness of the plate or column flange divided by the required thickness to develop the weld.

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11. Check column block shear ( = 0.75) Column - Flange Block Shear

There are four (4) shear planes plus (2) tension planes. Rn = (4)(0.6)Fytf[(bf - tw)/2 - k] +2UbsFutftp where: k = the corner clip = (k1 - tw/2) rounded up to the nearest in. Ubs = 1.0

12. Check the flexural strength of the bracket ( = 0.9) Built - Up Section - Flexure

Mn = FyZ where Z is the plastic section modulus of the bracket Mn Ru(Ws - N/2)

13. Check the flexural strength of the top and bottom single plates ( = 0.9) Built - Up - Seat/Bracket Plate Flexure The flexural strength of the top and bottom plates are checked for a uniform compression force exerted on them from the eccentric load on the bracket. .The plates are conservatively analyzed as simple beams spanning between the flanges of the column, span = (d - 2tf), and having a depth equal to (bf - tw)/2. The required moment, Mr, is taken as wL2/8, where w is the uniform flange force from the bracket.

w = Ru(Ws - N/2)/(Ls + tp)/(d - 2tf) Mr = wL2/8 where L = d - 2tf The available flexural strength of the plates is determined from the AISC Specifications Section F11. From AISC Section F11: (a) For rectangular bars with 0.08E/Fy < Lbd/t2 1.9E/Fy bent about their major axis:

ybn b y p2

FL dM = C 1.52 - 0.274 M MEt

AISC F11-2

and, (b) For rectangular bars with Lbd/t2 > 1.9E/Fy bent about their major axis: Mn = FcrSx Mp AISC F11-3 where

bcr

b2

1.9ECF =L dt

AISC F11-4

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Lb = length between points that are either braced against lateral displacement of the compression region, or between points braced to prevent twist of the cross section, in. Lb = (d - 2tf)/2 (supported by the column flanges and the bracket web). Lbd/t2 = Lbdp/tp2 where dp = depth of rectangular bar, in. = (bf - tw)/2 t = tp = width of rectangular bar parallel to axis of bending, in. Mp = FyZ Z = (tp)[(bf - tw)/2]2/4 My = FySx Sx = (tp)[(bf - tw)/2]2/6 Cb is conservatively taken as 1.0.

C. Bottom Chord Connection:

The bottom chord of the Joist Girder must be attached to the stabilizer plate to resist the chord force. In addition, the stabilizer plate must transfer this same force to the column. Stabilizer plates are normally sized based on a 3/4 in. thickness of plate. Using a 3/4 in. plate allows the plate to fit between the bottom chord angles allowing fillet welds to be made to the heels and toes of the chord angles. The Specifying Professional must specify that the Joist Girder bottom chords be a minimum thickness to accommodate the required weld size. As is required for the top chord, the Joist Girder Manufacturer has the responsibility to check the bottom chord angles for shear lag. Case 2 from Table D3.1 is applicable for this check. For reference, the shear lag factor is calculated for the bottom chord based on the INPUT of the angle size. Shear lag factors greater than 0.92 do not have an effect on the Joist Girders. Providing longer length fillet welds will reduce shear lag effects.

Stabilizer and Stiffener Checks:

Checks to be made:

1. Check stabilizer for yielding ( = 0.90) Stabilizer Plate - Yielding

Pu Rn Rn = tsWeffFy where ts = stabilizer thickness and Weff = stabilizer effective width Weff = the lesser of the Whitmore width or Wst.

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The Whitmore length equals (2)(tan30o)(Weld Length) + the bottom chord leg height. (AISC Manual Section 9-3).

2. Check stabilizer Block Shear Rupture Strength ( = 0.75)

Stabilizer Plate - Block Shear Rupture Strength AISC J4.3

(a) Block Shear Plane 1:

Rn = 0.60FuAnv + UbsFuAnt 0.60FyAgv + UbsFuAnt Anv = net area subject to shear, in.2 Ant = net area subject to tension, in.2 Ubs = 1.0

(b) Block Shear Plane 2: Checked as in (a).

3. Determine the weld between the bottom chord and the stabilizer plate ( = 0.75) Weld - Joist Girder Bottom Chord to Stabilizer Plate

Required length = Chord Force / Weld Strength = Pu / Rn Rn = 1.39D

4. Determine the Joist Girder shear lag factor Joist Girder - Shear Lag

xU 1

5. Shear Yielding in the Top and Bottom Stiffener Plates ( = 1.0) Stiffener Plate - Shear Yielding

k = corner clip = (k1 - tw/2) rounded up to nearest in. = 1.063 - 0.515/2 = 1.0 in. There are four shear planes Rn = (4)(0.6)(Fy)(tss)[(bf - tw)/2 - k]

6. Check the stiffener plates for flexure ( = 0.9)

Stiffener Plate - Flexure

The flexural strength of the stiffener plates are checked for concentrated compression force exerted on them from the stabilizer. The plates are analyzed as simple beams spanning between the flanges of the column, span = (d - 2tf), and having a depth equal to (bf - tw)/2. The required moment, Mr, per plate, is taken as PrL/4, where Pr is the force from the stabilizer.

Mr = PrL/4 where L = d - 2tf

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The available flexural strength of the plates is determined from the AISC Specifications Section F11. From AISC Section F11: (a) For rectangular bars with 0.08E/Fy < Lbd/t2 1.9E/Fy bent about their major axis:

ybn b y p2

FL dM = C 1.52 - 0.274 M MEt

AISC F11-2

And, (b) For rectangular bars with Lbd/t2 > 1.9E/Fy bent about their major axis:

Mn = FcrSx Mp AISC F11-3 where

bcr

b2

1.9ECF =L dt

AISC F11-4

Lb = length between points that are either braced against lateral displacement of the compression region, or between points braced to prevent twist of the cross section, in.

Lb = (d - 2tf)/2 (supported by the column flanges and the stabilizer). Lbd/t2 = Lbdp/tp2 where dp = depth of rectangular bar, in. dp = (bf - tw)/2 t = tss = width of rectangular bar parallel to axis of bending, in. Mp = FyZ Z = (tss)[(bf - tw)/2]2/4 My = FySx Sx = (tss)[(bf - tw)/2]2/6

Cb is conservatively taken as 1.0.

7. Check stiffener plate for shear rupture ( = 0.75)

Stiffener Plate - Shear Rupture AISC J4-4

There are two (4) shear planes Rn = (0.6)FuAnv Anv = 4(tss)(bf - tw)/2

8. Check Weld Stabilizer Plate to Top and Bottom Stiffener Plates ( = 0.75).

Weld - Stabilizer Plate to Stiffener Plates

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The stabilizer plate must be welded to the top and bottom plates to resist a tensile or compressive force. Four(4) welds resist the force.

Available weld length = 4(bf/2 - tw/2) Rn = (1.39)(D)(4)(bf/2 - tw/2)

9 . Check the welds between the stiffeners and the column flange ( = 0.75)

Weld - Stiffener to Column Flange

k = corner clip = k1 - tw/2 rounded up to nearest in. Weld length = (bf - tw)2 - k Eight (8) welds resist the force. Rn = 8(0.707)(wss)(0.6)(FEXX)(weld length)

10. Check column flanges for block shear ( = 0.75)

Column - Flange Block Shear

There are two (8) shear planes and 4 tension planes Rn = (8)(0.6)Fytf(bf - tw)/2 + 4Futftss

D. Minimum Member Thicknesses (Weld Compatibility):

Throughout the SPREADSHEET, checks are made for the minimum thicknesses of base metal to match the weld strength. From the AISC Specification, Section J2.4, The design strength, Rn and the allowable strength, Rn/ of welded joints shall be the lower value of the base material strength determined according to the limit states of tensile rupture and shear rupture and the weld metal strength determined according to the limit state of rupture as follows:

For the base metal: Rn = FnBMABM AISC J2-2

FnBM = nominal stress of the base metal (0.6Fu), ksi ABM = cross-sectional area of the base metal, in2. Rn = 0.6FuAnv AISC J4-4 Anv = net area subject to shear, in2. = 0.75 (LRFD), = 2.00 (ASD)

For the weld metal: Rn = 0.6FEXXAw

Aw = Area of the weld, in2. = 0.75 (LRFD), = 2.00 (ASD)

The compatibility check is done by comparing the weld strength (kips/in.) to the base metal strength (kips/in.). In LRFD terms:

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n weld n base metal

weld

base metal

cap u

R R= 0.75

= 0.751.39D kips / in 0.75 0.6 t F kips / in.

From Part 9 of the AISC Manual:

For fillet welds on one side of the connection:

minu

3.09D t =F

For fillet welds on both sides of the connection:

minu

6.19D t =F

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EXAMPLE: Given: W12x87 A992 Joist Girder Data (Factored Loads): d =12.50 in., bf = 12.10 in. Mu = 183 kip-ft. = 2196 kip-in. tw = 0.515 in., tf = 0.81 in. Pv = 90 kips k1 = 1.063 in. Joist Girder Depth = 36 in. Fy = 50 ksi 4x3/8 in. angle chords, gap = 1.0 in Fu = 65 ksi Column Cap Plate t = in. Fy plates = 36 ksi Bracket top and bottom plate thickness: 0.625 in. Fu plates = 58 ksi Bracket stiffener thickness: 0.75 in. Stabilizer Plate: 3/4x8x10 in. Bracket stiffener length: 12 in. Top Plate, Cap Plate and Cap Plate Weld:

Required top plate area = Pu/Fy. Pu = M/de = 2196/(36-2) = 64.6 kips. Ar = 64.6/(0.9)(36) = 1.99 in.2 (Fy = 36 ksi for the plate). Based on the 4.0 in. chord angles the width of the top chord would be 9 in. Try a plate, 1/2 x 4 in. The length of the plate is determined based on the required length of fillet welds used to attach the plate to the column cap plate and the top chord. Shear lag must be checked per the 2010 AISC Specification Table D3.1 Shear Lag Factors for Connections to Tension Members. The SPREADSHEET requires the weld length to be a minimum of two times the width of the plate. Based on Case 4 in Table D3.1, U =1.0, thus shear leg is not a factor in the top plate. Case 2 applies to the top chord angles. As noted earlier the Joist Girder Manufacturer is responsible for this check.

Try 1/4 in. fillet welds. The available force per inch of weld = Rn = (0.6 FEXX)(0.707)(1/4). Using FEXX = 70 ksi and = 0.75, Rn = 5.57 kips/in. Thus, a weld of 64.6/5.57/2 = 5.8 in. is required. Since the length of weld is less than two times the plate width shear lag must be taken into account. Use a weld length of 8 inches to avoid shear lag in the top plate at the Joist Girder top chord.

1. Check yielding ( = 0.9) Top Plate - Yielding Rn = FyAplate = (36)(0.5)(4) = 72 kips Rn = (0.9)(72) = 64.8 kips > 64.6 kips ok

2. Check tensile rupture

Top Plate - Tensile Rupture Shear lag at Joist Girder, U = 1.0 (Forced by the SPREADSHEET) Shear lag at the cap plate: lcp = 8 in., Wtp = 4.0 in., lcp 2Wtp therefore U= 1.0

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Rn = UFuAplate = (1.0)(58)(0.5)(4) = 116 kips kips Rn = (0.75)(116) = 87 kips > 64.6 kips ok

3. Determine the shear yielding strength of the column ( = 0.9) Column - Shear Yielding

Vn = 0.6FyAfCv Af = 2bftf Cv= 1.0 Vn = (0.6)(50) (2)(12.10)(0.810)(1) = 588.1 kips Vn = (0.9)(588.1) = 529.3 kips > 64.6 kips ok

4. Determine the Joist Girder top chord shear lag factor

Joist Girder - Shear Lag

.

2 2tc tc tc tc

bartc tc

B + t B - t 4 + 0.3125 4.0 - 0.3125x = = = 1.116 in

2 2B - t 2 2 4.0 - 0.3125

x .U . 1 1161 1 0 868

5. Determine the weld strength between the Joist Girder and the top chord ( = 0.75) Weld - Top Plate to Joist Girder Top Chord Rn = (0.6)(FEXX)(0.707)wtc = (0.6)(70)(0.707)(0.25) = 7.424 kips/in. Rn = (0.75)(7.42) = 5.57 kips/in Strength = Rn = (2)( Rn)(Ltc) = (2)(5.57)(8) = 89.1 kips 64.6 ok

6. Determine the weld strength between the top plate and the column cap ( = 0.75) Weld - Top Plate to Column Cap Plate Strength = Rn = (2)( Rn)(Lcp) = (2)(5.57)(8) = 89.1 kips 64.6 ok

7. Weld strength between the column cap plate and the column flanges ( = 0.75) Column Cap Plate - Weld to Column Flanges

Rn = (0.707)(wccp)(0.60)(FEXX)(2bf) = (0.707)(0.25)(0.60)(70)(2)(12.10) = 179.6 kips Rn = (0.75)(179.6) = 134.7 kips 64.6 kips ok

Design the seat bracket for the 90 kip vertical reaction.

1. Minimum bracket plate and stiffener thickness = 0.5 in.

2. Determine the maximum bracket height

Joist Girder depth - the Joist Girder seat height - of the stabilize width top and bottom plate thicknesses - 6 in. clearance.

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Max bracket height 36 - 7.5 - 4 - 2 - 6 = 16.5 in.

3. Local buckling of the bracket plates Local Buckling The seat plate width, b = (d - 2bf)/2 b = [12.5 - (2)(0.810)]/2 = 5.44 in. Try a stiffener height (L s) equal to 12 in. For the top and bottom plates of the bracket:

p y

b E 29000 0.38 = 0.38 =10.8t F 36

tpmin = 5.44/10.8 = 0.504 in. 5/8 in. ok

For the web of the bracket (vertical stiffener):

s y

h E 29000 3.76 = 3.76 =106t F 36

tsmin = 12.0/106 = 0.11 in.

tsmin = 0.5 in. 5/8 in. plate is ok.

4. Check the seat plate for shear yielding from the Joist Girder reaction ( = 1.0).

Seat Plate - Shear Yielding

u

py

P 90t = = 0.5208 in.1.0 2 4 0.6 362 N 0.6F

Use 5/8 horizontal plates

5. Required thickness of the seat plate due to uplift ( = 0.9) Seat Plate - Uplift Loading

beff = (g - ts) N = 5.0 - 0.50 = 4.50 > 4.00, beff = 4.00 in. Mn = FyZ 1.6My Mn = Fybefftp2/4 1.6Fybefftp2/6 = (36)(4)(0.625)2/4 < (1.6)(36)(4)(0.625)2/6 = 14.1 15.0 kip-in. Mn = 14.1 kip-in. per side Mn = (0.9)(14.1) = 12.69 kip-in. per side Lever arm = (Bolt gage ts)/2 = (5.0 - 0.5)/2 = 2.25 in. Rn = 2Mn/Lever arm = (2)(12.69)/2.25 = 11.3 kips

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6. The stiffener bearing strength on the contact area must satisfy 2010 AISC Specification Chapter J Section J7(a) ( = 0.75) Stiffener - Bearing Strength on Contact Area

pbyn AF8.1R

where, Apb = projected bearing area, in.2 (mm2) Fy = specified minimum yield stress, ksi (MPa) Rn = (0.75)(1.8)(36)(4)(0.50) = 97.2 kips > 90 kips o.k.

7. Check the stiffener for shear yielding ( = 1.0)

Stiffener - Shear Yielding Try a stiffener length (Ls) of 12 in.

u

wy s

P 90t = = 0.35 in.1.0 0.6 36 12.00.6F L

Rn = (0.6)(Fy)(Ls)(ts) = (0.6)(36)(12.0)(0.50) = 129.6 kips Rn = 129.6 90 kips ok

8. Required weld connecting the vertical stiffener to the column web ( = 0.75) Weld - Stiffener to Column Web Ru Rn Rn = (2)(0.75)(0.6)FEXX(0.707)(ws)(Ls) Try in. fillet, Ls =12 in. each side of web. Rn = (2)(0.75)(0.6)(70)(0.707)(.25)(12) = 133.6 kips. 90 133.6 ok Use in. fillet welds

9. Required weld connecting the stiffener to the horizontal plates ( = 0.75)

Weld - Stiffener to Seat/Bracket Plates

Shear Flow: From the bracket dimensions: I = 614 in4, Q = 42.93 in3 Ruh = q = VQ/I = (90)(42.93)/614 = 6.288 kips/in.

For uplift case: beff = (5.0 - 0.50)/2 = 4.50 in. 4 beff = 4 in. (Controls) Ruv = Ru/beff = 20/8 = 2.5 kips/in. Ruh = q = VQ/I = (20)(42.93)/614 = 1.40 k/in.

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Weld Resultant: . . . . 2 22 2u uv uhR = R +R 2 5 + 1 40 2 87 kips / in The nominal strength of the weld, kips/in. is calculated from the equation: Rn = (2)(0.6)(FEXX)(0.707)(ws) = (2)(0.6)(70)(0.25) = 14.8 kips/in. Rn = (0.75)(14.8) = 11.14 kips/in. 11.14 kips/in. > 6.288 kips/in. ok

Use 1/4 in. fillet weld.

10. Strength of the welds connecting the seat bracket plates to the column flange, and the minimum thickness of the plates and column flange ( = 0.75) Weld - Seat/Bracket Plates to Column Flange

Vr = (Ru)(Ws - N/2)/(Ls + tp) kips/top or bottom plate = (90)(12 - 2)/(12.0 + 0.625) = 71.3 kips k = k1 - tw/2 = 1.063 - 0.515/2 = 0.8055 in. rounded up to nearest in. = 1.00 in. Weld Length = (bf - tw)/2 - k = (12.1 - 0.515)/2 - 1.00 = 4.7925 in. Rn = (4)(0.6)(FEXX)(0.707)(wp)(Weld Length) = (4)(0.6)(70)(0.707)(0.25)(4.7925) = 142.3 kips Rn = (0.75)(142.3) = 106.7 kips Vr Rn 106.7 kips > 71.3 kips ok

11. Check column flange for block shear ( = 0.75)

Column - Flange Block Shear There are four (4) shear planes and two (2) tension planes Rn = (4)(0.6)Fytf[(bf - tw)/2 - k] +2UbsFutftp k = the corner clip = (k1 - tw/2) rounded up to the nearest in. k = 1.063 - 0.515/2 = 0.8055 in. rounded up to 1.0 in. Rn = (2.4)(50)(0.810)[(12.10 - 0.515)/2 -1.0] + (2)(1.0)(65)(0.810)(0.625) = 531.6 kips Rn = (0.75)(531.6) = 398.7 kips 71.3 ok

12. Check the flexural strength of the bracket ( = 0.9)

Built - Up Section - Flexure Mn = FyZ = (36)(103.9) = 3740.4 kip-in. where Z is the plastic section modulus of the bracket (Cell R41) Mn = (0.9)(3740.4) = 3366 kip-in. Mn Ru(Ws - N/2) 3366 kip-in. (90)(12.0 - 4/2) = 900 kip-in. ok

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13. Check the flexural strength of the top and bottom single plates ( = 0.9) Built - Up - Seat/Bracket Plate Flexure w = (Ru)(Ws - N/2)/(Ls + tp)/(d - 2tf) = (90)(12.0 - 4/2)/(12.0 + 0.625)/[12.5 - (2)(0.81)] = 6.55 kips/in. Mr = wL2/8 = (6.55)(d - 2tf)2/8 = (6.55)[(12.5 - (2)(0.810)]2/8 = 96.9 kip-in. From AISC Section F11-2: (a) For rectangular bars with 0.08E/Fy < Lbd/t2 1.9E/Fy bent about their major axis: Lb = (d - 2tf)/2 = [(12.5 - (2)(0.81)]/2 = 5.44 in. dp = (bf - tw)/2 = (12.1 - 0.515)/2 = 5.79 in. Lbdp/t2 = (5.44)(5.79)/(0.625)2 = 80.6 0.08E/Fy < Lbd/t2 1.9E/Fy, 64.44 < 80.6 1530 therefore:

ybn b y p2

FL dM = C 1.52 - 0.274 M MEt

t = tp = 0.625 in. Z = (tp)[(bf - tw)/2]2/4 = (0.625)[(12.1 - 0.515)/2]2/4 = 5.24 in3 Mp = FyZ = 188.7 kip-in Sx = (tp)[(bf - tw)/2]2/6 = (0.625)[(12.1 - 0.515)/2]2/6 = 3.50 in3 My = FySx = 125.8 kip-in

. .

n y p

n y

36M = 1 0 1.52 - 0.274 80 67 M M29000

M = 1.49M = 1.49 125.8 = 187.4 188.7 kip - in

Mn = (0.9)(187.4) = 169 kip-in > 96.9 kip-in. ok By observation controls over Uplift Case.

Bottom Chord Checks:

1. Check stabilizer for yielding ( =0.90) Stabilizer Plate - Yielding Rn = t stW effFy

The Whitmore length equals (2)(tan30o)(8) = 9.24 in. plus the bottom chord leg length. Thus the Whitmore width = 9.24 + 4 = 13.2 in. > 8 in. Weff = 8.0 in. Rn = (0.75)(8)(36) = 216.0 kips Rn = (0.9)(216.0) = 194.4 kips 194.4 64.6 kips ok

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2. Check stabilizer block shear rupture strength ( = 0.75) Stabilizer Plate - Block Shear Rupture Strength (c) Block Shear Plane 1: Rn = 0.60FuAnv + UbsFuAnt 0.60FyAgv + UbsFuAnt Anv = Agv = (2)(8)(0.75) = 12.0 in.2 Ant = (4)(0.75) = 3.0 in.2 Rn = (0.60)(58)(12.0)+(1.0)(58)(3.0) (0.6)(36)(12.0)+(1.0)(58)(3.0) = 592 433 kips, Rn = 433 kips

(d) Block Shear Plane 2:

Anv = Agv = (8)(0.75) = 6.0 in.2 Ant = [Angle leg length + (Wst - Angle leg length)/2]tst =[4 + (8 - 4)/2](0.75) = 4.5 in. Rn = (0.60)(58)(6.0) + (1.0)(58)(4.5) (0.6)(36)(6.0)+(1.0)(58)(4.5) = 470 391 kips, Rn = 391 kips Rn = (0.75)(391) = 293 64.6 kips ok

3. Determine the weld between the bottom chord and the stabilizer plate ( = 0.75) Weld - Joist Girder Bottom Chord to Stabilizer Plate

Try 1/4 in. fillet welds: Rn = (1.392)(4) = 5.57 kips/ in. Required length = 64.6/5.57 = 11.6 in.

The welds must be 8 in. long (2 times the bottom chord leg height) to avoid a shear lag reduction for the stabilizer. Rn = (0.75)(5.57)(4)(8) = 133.6 kips > 64.6 ok Use 4-1/4 in. fillet welds 8 in. long The Specifying Professional must request that the Joist Girder bottom chords be a minimum of 5/16 in. thickness. The Joist Girder Manufacturer is responsible for the shear lag check of the bottom chord.

4. Determine the Joist Girder shear lag factor

Joist Girder - Shear Lag Eccentricity, x = 1.116

x .U . 1 1161 1 0 868

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5. Shear Yielding in the Top and Bottom Stiffener Plates ( = 1.0) Stiffener Plate - Shear Yielding Corner clip = (k1 - tw/2) rounded up to nearest in. = 1.063 - 0.515/2 = 0.8055 in. Rounded up to 1.0 in. There are four shear planes Rn = (4)(0.6)(Fy)(tss)[(bf - tw)/2 - k] = (1.0)(4)(0.6)(36)(0.50)[(12.10 - 0.515)/2 - 1.0] = 207 kips Ru = 64.6 kips 207 kips > 64.6 kips ok

6. Check the stiffener plates for flexure ( = 0.9) Stiffener Plate - Flexure From AISC Section F11: (a) For rectangular bars with 0.08E/Fy < Lbd/t2 1.9E/Fy bent about their major axis: Lb = (d - 2tf)/2 = [(12.50 - (2)(0.81)]/2 = 5.44 in. dp = (bf - tw)/2 = (12.10 - 0.515)/2 = 5.79in. Lbdp/tss2 = (5.44)(5.79)/(0.5)2 = 126 0.08E/Fy < Lbd/t2 1.9E/Fy, 64.44 < 126 1530 therefore:

ybn b y p2

FL dM = C 1.52 - 0.274 M MEt

Z = (tss)[(bf - tw)/2]2/4 = (0.50)[(12.1 - 0.515)/2]2/4 = 4.19 in3 Mp = FyZ = 151 kip-in. Sx = (tss)[(bf - tw)/2]2/6 = 2.796 My = FySx = 100.7 kip-in.

.

n y p36M = 1 0 1.52 - 0.274 126 M M

29000

Mn = 1.477My = (1.48)(100.7) = 148.7 kip-in. per plate Mn = RnL/4, Rn = 4Mn/L = (4)(0.9)(148.7)/10.88 = 49.2 kips/plate For two plates Rn = 98.41 kips where L = d - 2tf = 12.5 - (2)(0.81) = 10.88 in. For two plates: Rn = 98.4 kips 98.4 > 64.6 ok

7. Check the stiffener plate for shear rupture ( = 0.75) Stiffener Plate - Shear Rupture

Anv = 4(tss)(bf - tw)/2 = (4)(0.50)(12.10 - 0.515)/2 = 11.585 in2 Rn = (0.6)FuAnv = (0.6)(58)(11.585) = 403.16 kips Rn = (0.75)(403.16) = 302.4 kips > 64.6 kips ok

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8. Check the weld from between the stabilizer plate and the stiffener plates ( =0.75). Weld - Stabilizer Plate to Stiffener Plates

The stabilizer plate must be welded to the top and bottom plates to resist a tension or compression force of 64.6 kips. Available weld length = 4(bf/2 - tw/2) = (4)(12.10 - 0.515)/2 = 23.17 in. Try 1/4 in. fillet welds: Rn = (1.39)(4)(23.17) = 129 kips > 64.6 kips ok Use 4-1/4 in. fillet welds 5 in. long, ok by inspection.

9. Check the weld between the stiffener and the column flange ( = 0.75). Weld - Stiffener to Column Flange k = corner clip = k1 - tw/2 rounded up to nearest in. = 1.063 - 0.515/2 = 0.8055 in. Rounded up to 1.0 in. Weld length = (bf - tw)2 - k = (12.10 - 0.515)/2 - 1.0 = 4.7925 in. Eight (8) welds resist the force. Rn = 8(0.707)(wss)(0.6)(FEXX)(weld length) = (8)(0.707)(0.1875)(0.6)(70)(4.7925) = 213.5 kips Rn = (0.75)(213.5) = 160.1 kips > 64.6 kips ok

10.0 Check column flanges for block shear ( = 0.75) Column - Flange Block Shear k = k1 - tw/2 rounded up to nearest in. = 1.063 - 0.515/2 = 0.8055 in. = 1.0 in. Rn = (8)(0.6)Fytf[(bf - tw)/2 k] + 4Futftss = (8)(0.6)(50)(0.810)[(12.10 - 0.515)/2 - 1.0] + (4)(65)(0.810)(0.500) = 1037 kips Rn = 0.75(1037) = 777.7 kips 64.6 ok

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PROGRAM USAGE GUIDE Joist Girder Connections to the Weak Axis of Wide Flange Columns

SPREADSHEET Philosophy: The SPREADSHEET is structured to allow the user to input all data rather than forcing computer generated values. This allows the user to select values or to use office standards. This is especially useful when a multitude of designs are being considered so that calculations can be provided for lumping common values. SPREADSHEET Description: The SPREADSHEET has seven sheet tabs consisting of General Information, Formatting, Sidewall W Column Diagram, Moment - Sidewall W Column, Interior W Column Diagram, Moment - Interior W Column, and AISC Database v14.

General Information - List of design references, explanation of LFRD and ASD color coding.

Formatting - Information on the printing formatting setup for the SPREADSHEET.

Sidewall W Column Diagram - A diagram of the connection being designed for a Joist Girder to a sidewall W column (with nomenclature).

Moment-Sidewall W Column - Design input and output sheet for the moment connection for a Joist Girder to a sidewall W column.

Interior W Column Diagram - A diagram of the connection being designed for Joist Girder to an interior W column (with nomenclature).

Moment-Interior W Column - Design Input and Output sheet for the moment connection for two Joist Girders to an interior W column.

ASIC Database v14 - AISC shape data for use in the connection design.

The actual design input and output sheets have been formatted to print all required information for the design calculations of the connections.

SPREADSHEET Usage: Before using the SPREADSHEET you should have in your possession:

1. The Steel Joist Institutes Technical Digest 11, Design of Lateral Load Resisting Frames Using Steel Joists and Joist Girders.

2. The Steel Joist Institutes Technical Digest 6, Design of Steel Joist Roofs to Resist Uplift Loads.

3. ANSI/AISC 360- 10, Specification for Structural Steel Buildings. 4. The Steel Joist Institutes Standard Specification for Joist Girders, 2010. 5. Frame analysis results, such as Joist Girder end reactions, connection moments,

and column axial loads.

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First read the General Information Tab and the Formatting Tab.

Print out the diagrams: Sidewall W Column Diagram and the Interior W Column Diagram. These will assist you with input requirements. For proper printing of the SPREADSHEET you may have to reset the margins.

PRELIMINARY DESIGN WORK: The user can use trial and error to obtain an adequate connection design; however, it is generally beneficial to do some preliminary sizing of certain input values. An example is provided at the end of this section as a reference.

Joist Girder Data: Typically at the early stage of the design the actual Joist Girder design is not known by the user. The user can either estimate the Joist Girder chords, weights and seat sizes, or they can contact a SJI member company for the information. If the Joist Girder data is unknown the following information can be estimated:

The chord sizes can be estimated as described in Chapter 2 of the SJI Technical Digest 11.

The Joist Girder weight can be estimated using the SJI tabulated values in the published catalog, or by multiplying the top or bottom chord weight by 2.5. See the PRELIMINARY SIZING EXAMPLE.

The seat size can be estimated using the standards set forth by SJI Standard Code of practice suggested sizes based on Joist Girder weight.

Top Plate Preliminary Sizing: The maximum width of the top plate, W tp, is 2 times the chord angle leg size plus the 1 in. gap minus the shelf dimension for the welds.

Minimum Weld Shelf Dimensions Field Weld Size, in. Minimum Shelf Dimension, in

3/16 7/16 1/4 1/2 5/16 9/16 3/8 5/8 7/16 11/16 1/2 3/4

Table 1 Minimum Weld Shelf Dimensions

The preliminary thickness of the top moment plate, t tp, can be calculated by:

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1. First determining the chord force in the Joist Girder. The chord force is obtained by dividing the end moment of the Joist Girder by the effective depth (Joist Girder depth - of the bottom chord angle size).

2. Then adding any additional axial chord load. 3. The plate thickness can then be determined by dividing the chord force by the

desired width of the top plate and Fy (LRFD) or 0.6Fy (ASD). Stabilizer Plate Preliminary Sizing: An initial thickness of the stabilizer plate, t st, is determined based on the 1 in. standard gap between the Joist Girder chord angles. Typically a 3/4 in. thickness is used to allow tolerance for field erection and still allow for fillet welds from the chord angles to the plate.

The width of the stabilizer plate (W st) is estimated by dividing the required axial force (see Top Plate Preliminary Sizing) by the thickness of the stabilizer plate and Fy (LRFD) or 0.6Fy (ASD). The stabilizer width must be a minimum of the chord angle leg size plus the weld shelf dimensions.

Bracket Connection: Determining the maximum length of the stiffener saves later checking during the design process. The maximum Stiffener Length (L s) is approximately equal to the Joist Girder depth minus the (Joist Girder seat depth + the horizontal plate thicknesses + 1/2 the stabilizer plate vertical width + 6 in. clearance). The Joist Girder seat depth is 7 1/2 in. on Joist Girders weighing 50 plf or less and 10 in. for Joist Girders having a weight over 50 plf. The Horizontal Plate Thicknesses (tp) can be estimated at 1 in. for this calculation.

INPUT: Use the Tabs to select a Moment- Sidewall W Column Design, or a Moment- Interior W Column Design. If an interior column only has one side with a moment connection, use the Moment-Sidewall W Column Tab.

All yellow filled cells are required input.

There are two pull down Tabs, one used to select whether you want an LRFD or an ASD Design and the second to choose the size of the W column for the design.

The CLEAR buttons can be used to clear all of the input cells in the group. There is one button for connection input and one for the loading input. This CLEAR button does not clear the project information, i.e., project name, number or engineer.

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COLUMN DATA: Column data is automatically obtained from a file of the AISC W-Shapes after using the drop down tab, or by typing in the column size. JOIST GIRDER DATA: For preliminary design, if the Joist Girder properties are not known, the chord sizes can be estimated as described in Chapter 2 of the SJI Technical Digest 11. If you conducted your analysis using the SJI Virtual Joist Girder Tables you can also obtain the Joist Girder weight from your analysis. JOIST GIRDER & COLUMN DESIGN LOAD DATA: Fill in the values indicated in the Table. Values must be consistent with the type of design you have selected, i.e. LRFD or ASD. Up to six load cases are permitted per design. The column axial load is the total axial load on the column and must include the reaction(s) of the Joist Girder(s).

REMARKS INDICATED ON THE INPUT DATA: (1) See SJI Specifications for minimum: Applies to the Bearing Seat Length (N) and

Bearing Seat Width (W s). The 2010 SJI Specifications, Section 1004.4(b), indicate that, the minimum bearing length is 4 inches, and the 2010 SJI Code of Standard Practice indicates that, Joist Girder bearing seat widths vary depending on the Joist Girder size and shall be permitted to be up to 13" wide. It is recommended that the minimum Bearing Seat Length be increased to 6" for Joist Girders weighing more than 50 pounds per foot, and that the Bearing Seat Width be 9" for Joist Girders weighing less than 50 pounds per foot and be 13" for Joist Girders weighing more than 50 pounds per foot. The Joist Girder weight can be estimated from the SJI Catalog values or by multiplying the bottom chord weight by 2.5.

(2) Not to encroach on stabilizer: The bracket cannot encroach on the stabilizer plate. This must be manually checked. See comment for Bracket Connection on the previous page. (3) Less than JG TC width minus weld shelf dimensions: The Joist Girder (JG) Top Plate Width (W tp) must be less than the top chord (TC) width minus the shelf dimension for the fillet welds connecting the Top Plate to the Top Chord, i.e. 2 times the chord angle size plus the 1 in. gap minus the shelf dimensions.

(4) Includes Joist Girder end reactions: The Column Axial Load, Pu (LRFD) or Pa (ASD), is to include the end reaction(s) of the Joist Girder(s).

29

DESIGN REVIEW: Examine the SUMMARY RESULTS for MOMENT CONNECTION to determine if the design criteria are satisfied, or if undo conservatism exists relative to any of the input data. The DETAILED RESULTS for MOMENT CONNECTION provides minimum design criteria, the nominal strength, and the Design Strength (LRFD) or the Allowable Strength (ASD) for the input data. These values can be studied to determine input refinements. You can then make any necessary input changes.

PRELIMINARY SIZING EXAMPLE: For a 36 in. deep Joist Girder spanning 40 ft. with an end moment of 183 kip-ft. and a panel point load of 18 kips (factored). The end reaction is 90 kips. The Joist Girder frames to the weak axis of a W12x87 column.

Pchord = (12)(183)/(36 - 2) = 64.6 kips From SJI TD 11, Table 2-1 (LRFD), Fy = 50 ksi, = 0.90)

Table 2-1 (Partial) Double Angle Chord Available Strength (LRFD) for Various Unbraced Lengths, kips

2Ls: 2-1/2 x 2-1/2 x 1/4 would be sufficient; however, gravity loads would control the size. Try 2Ls 4x4x3/8. Area = 5.72 in2. Estimate the Joist Girder weight: From the SJI Catalog 47 plf.

From the chord size, the Joist Girder weight = (2.5)(3.4)(5.72) = 48.6 plf So conservatively assume the Joist Girder weight = 53 plf

Angle Size Unbraced Length Area L = 5 ft. in.2

2L 3 x 3 x 1/4 87 2.87 2L 3 x 3 x 3/16 49 2.18 2L 2-1/2 x 2-1/2 x 1/2 124 4.50 2L 2-1/2 x 2-1/2 x 3/8 97 3.47 2L 2-1/2 x 2-1/2 x 5/16 83 2.93 2L 2-1/2 x 2-1/2 x 1/4 68 2.37 2L 2-1/2 x 2-1/2 x 3/16 48 1.80

30

Estimate the BRACKET Top Plate Width (Wp) based on SJI standards: Weight = 53 plf; therefore, the Seat Plate Width (W p) = 9 in.

For the Top Plate assume a 1/4 in. fillet weld is used to attach the plate. A 1/2 in. weld shelf dimension is required.

Preliminary Top Plate size: W tp = 1+2(4.0 - 0.5) = 8 in. maximum

Try W tp = 4 in.

t tp = (64.6)/[(0.9)(4)(36)] = 0.50 in., Try 1/2 in.

Preliminary Stabilizer Plate Width (Wst): t st = 3/4 in. for a 1 in. gap between chords

W st = (64.6)/[(0.9)(0.75)(36)] = 2.65 in. Use a 8 in. plate 8 in. [4.0+(2)(0.5)] = 5.0 in. ok

Determine the Maximum Stiffener Length (L s) for the Stiffened Seat Connection:

Ls = 36 - (7.5+2 + (8/2) + 6) = 16.5 in so maximum stiffener length is 16 in.